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Abstract

Particle Swarm Optimization (PSO) is an evolutionary optimization algorithm inspired by the social behavior of birds flocking and fish schooling. Numerous PSO variants have been proposed in the literature for addressing different problem types. In this chapter, the authors apply different PSO variants to common antenna and microwave design problems. The Inertia Weight PSO (IWPSO), the Constriction Factor PSO (CFPSO), and the Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithms are applied to real-valued optimization problems. Correspondingly, discrete PSO optimizers such as the binary PSO (binPSO) and the Boolean PSO with velocity mutation (BPSO-vm) are used to solve discrete-valued optimization problems. In case of a multi-objective optimization problem, the authors apply two multi-objective PSO variants. Namely, these are the Multi-Objective PSO (MOPSO) and the Multi-Objective PSO with Fitness Sharing (MOPSO-fs) algorithms. The design examples presented here include microwave absorber design, linear array synthesis, patch antenna design, and dual-band base station antenna optimization. The conclusion and a discussion on future trends complete the chapter.

Introduction

In the past decade, several evolutionary algorithms (EAs) that mimic the behavior and evolution of biological entities emerged. Among others, Particle Swarm Optimization (PSO) is a popular evolutionary algorithm which is based on the intelligence and movement of swarms (birds, fishes, bees, etc.) and resembles their behavior (Kennedy & Eberhart, 1995).

Many similarities exist between PSO and other evolutionary computation techniques such as Genetic Algorithms (GAs). In general, PSO does not have any evolution operators like crossover and mutation. Compared to Genetic Algorithms, PSO has fewer parameters to adjust and is easier to implement in any programming language. PSO is also computationally more efficient than a GA with the same population size. The algorithm has been successfully applied in many engineering disciplines: function optimization, artificial neural network training, fuzzy system control and other areas where GAs are also applied. The fact that particle swarm optimizers can handle efficiently arbitrary optimization problems has also made them popular for solving problems in electromagnetics, especially in electromagnetic design ones (Baskar, Alphones, Suganthan, & Liang, 2005; Deligkaris et al., 2009; Goudos, Moysiadou, Samaras, Siakavara, & Sahalos, 2010; Goudos, Rekanos, & Sahalos, 2008; Goudos & Sahalos, 2006; Goudos, Zaharis, Kampitaki, Rekanos, & Hilas, 2009; Khodier & Christodoulou, 2005; Robinson & Rahmat-Samii, 2004; Zaharis, 2008; Zaharis, Kampitaki, Lazaridis, Papastergiou, & Gallion, 2007). Numerous different PSO variants exist in the literature. The most common algorithms include the classical Inertia Weight PSO (IWPSO) and the Constriction Factor PSO (CFPSO) (Clerc, 1999). However, in order to further improve the performance of PSO on complex multimodal problems, a PSO variant was proposed (Liang, Qin, Suganthan, & Baskar, 2006). This variant is the Comprehensive Learning Particle Swarm Optimizer (CLPSO) which utilizes a new learning strategy. The CLPSO algorithm accelerates the convergence of the classical PSO. It has been applied successfully to Yagi-Uda antenna design by Baskar et al. (2005) and to linear array synthesis by Goudos et al. (2010).

The PSO algorithm is inherently used only for real-valued problems but can easily expand to discrete-valued problems. A simple modification of the real-valued PSO called binary PSO (binPSO) has been presented by Kennedy & Eberhart (1997). In (Marandi, Afshinmanesh, Shahabadi, & Bahrami, 2006) the Boolean PSO is introduced and applied to dual-band planar antenna design. The Boolean PSO is based on the idea of using exclusively Boolean update expressions in the binary space. An extension to Boolean PSO, that improves the algorithm performance, is the Boolean PSO with velocity mutation (BPSO-vm) which has been applied successfully to patch antenna design (Deligkaris et al., 2009).